Details

Time bar (total: 7.3s)

sample52.0ms

Algorithm
intervals
Results
11.0ms159×body160valid
9.0ms504×pre80true
8.0ms248×body80nan
5.0ms46×body320valid
2.0ms51×body80valid

simplify50.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (5.0ms)

IterNodesCost
01417
12517
24516
38716
410616
511416
done11416

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b
(- (* b b) (* (* 4.0 a) c))
0.2b
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
38.7b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
19×prod-diff
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×fma-neg
5×pow1 div-inv
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-/r* flip--
2×sub-neg sqrt-div diff-log div-sub
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 183
Calls
4 calls:
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
3.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
24.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

series299.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
44.0ms
(- (* b b) (* (* 4.0 a) c))
106.0ms
(/ (/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0) a)
80.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)

simplify986.0ms

Counts
195 → 195
Iterations

Useful iterations: done (979.0ms)

IterNodesCost
03214967
17804592
230174265
done50014264

prune487.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.7b

localize3.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000
done00

prune52.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 4.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (* a c) b)
0.2b
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
27×add-exp-log add-cbrt-cube
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-undiv div-exp
8×associate-/l*
6×associate-/r* div-inv
5×prod-exp cbrt-unprod
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
2 → 77
Calls
2 calls:
3.0ms
(/ (* a c) b)
10.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

series42.0ms

Counts
2 → 6
Calls
2 calls:
19.0ms
(/ (* a c) b)
23.0ms
(/ (/ (* -2.0 (/ (* a c) b)) 2.0) a)

simplify739.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (146.0ms)

IterNodesCost
01711200
14591154
22313992
done5000992

prune233.0ms

Pruning

32 alts after pruning (31 fresh and 1 done)

Merged error: 4.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ a (sqrt b))
0.2b
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
0.3b
(/ c (sqrt b))
0.3b
(* (/ a (sqrt b)) (/ c (sqrt b)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
117×times-frac
106×add-sqr-sqrt
76×add-cube-cbrt *-un-lft-identity
53×add-exp-log add-cbrt-cube
48×sqrt-prod
23×cbrt-undiv div-exp
22×associate-*r* associate-*l*
15×associate-/r*
13×prod-exp cbrt-unprod associate-/l*
9×div-inv unswap-sqr
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
4 → 215
Calls
4 calls:
3.0ms
(/ a (sqrt b))
25.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
3.0ms
(/ c (sqrt b))
25.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

series164.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ a (sqrt b))
38.0ms
(/ (/ (* -2.0 (* (/ a (sqrt b)) (/ c (sqrt b)))) 2.0) a)
42.0ms
(/ c (sqrt b))
42.0ms
(* (/ a (sqrt b)) (/ c (sqrt b)))

simplify1.7s

Counts
227 → 227
Iterations

Useful iterations: 2 (363.0ms)

IterNodesCost
03653367
110303167
249302435
done50002435

prune443.0ms

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 4.5b

regimes375.0ms

Accuracy

0% (7.1b remaining)

Error of 12.2b against oracle of 5.0b and baseline of 12.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055
165
done65

end0.0ms

sample1.5s

Algorithm
intervals
Results
341.0ms4829×body160valid
304.0ms16283×pre80true
278.0ms8283×body80nan
142.0ms1358×body320valid
64.0ms1813×body80valid